When a borrower becomes insolvent and the loan cannot be repaid, the lender records it on their books as a loss. They cannot just pretend the loan never happened.
Of course, now we’re mixing subjects because OP asked about student loan forgiveness, which would necessarily come out of tax payers’ pockets (not the same as when a lender takes the L because the loan cannot be repaid).
Fractional reserve banking does not mean the debt does not exist. The debt very much exists. Nobody takes out a loan and just sits on it. As soon as the loan is created, goods and services are traded. At the end of the day, each party to downstream transactions can go to the bank and withdraw the balance of their account in cash. The fractional reserve system only works as long as not everyone does this at once.